x2 - 12x + 10 factorization
Answers
Answer:
Simplifying
x2 + -12x + 10 = 0
Reorder the terms:
10 + -12x + x2 = 0
Solving
10 + -12x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '-10' to each side of the equation.
10 + -12x + -10 + x2 = 0 + -10
Reorder the terms:
10 + -10 + -12x + x2 = 0 + -10
Combine like terms: 10 + -10 = 0
0 + -12x + x2 = 0 + -10
-12x + x2 = 0 + -10
Combine like terms: 0 + -10 = -10
-12x + x2 = -10
The x term is -12x. Take half its coefficient (-6).
Square it (36) and add it to both sides.
Add '36' to each side of the equation.
-12x + 36 + x2 = -10 + 36
Reorder the terms:
36 + -12x + x2 = -10 + 36
Combine like terms: -10 + 36 = 26
36 + -12x + x2 = 26
Factor a perfect square on the left side:
(x + -6)(x + -6) = 26
Calculate the square root of the right side: 5.099019514
Break this problem into two subproblems by setting
(x + -6) equal to 5.099019514 and -5.099019514.
Subproblem 1
x + -6 = 5.099019514
Simplifying
x + -6 = 5.099019514
Reorder the terms:
-6 + x = 5.099019514
Solving
-6 + x = 5.099019514
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6' to each side of the equation.
-6 + 6 + x = 5.099019514 + 6
Combine like terms: -6 + 6 = 0
0 + x = 5.099019514 + 6
x = 5.099019514 + 6
Combine like terms: 5.099019514 + 6 = 11.099019514
x = 11.099019514
Simplifying
x = 11.099019514
Subproblem 2
x + -6 = -5.099019514
Simplifying
x + -6 = -5.099019514
Reorder the terms:
-6 + x = -5.099019514
Solving
-6 + x = -5.099019514
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6' to each side of the equation.
-6 + 6 + x = -5.099019514 + 6
Combine like terms: -6 + 6 = 0
0 + x = -5.099019514 + 6
x = -5.099019514 + 6
Combine like terms: -5.099019514 + 6 = 0.900980486
x = 0.900980486
Simplifying
x = 0.900980486
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.099019514, 0.900980486}